After adding your custom control class, you need to register your control like below code, then you can call your control via JS

$wp_customize->register_control_type( 'TestControl' );

After adding your custom control class, you need to register your control like below code, then you can call your control via JS

function prefix_customize_register( $wp_customize ) {
    $wp_customize->register_control_type( 'TestControl' );
}
add_action( 'customize_register', 'prefix_customize_register' );

Then via JS, like this:

api.control.add(
    new api.Control( 'birthdate', {
      type: 'test-control',
      label: 'Birthdate',
      description: "Someone was born on this day.",
      section: 'my_custom_section',
      includeTime: false,
      setting: new api.Value('2000-01-02')
    })
);